Let $(x+a)$ be the HCF of $x^2+px+q$ and $x^2+mx+n$. Show that $a=(q-n)/(p-m)$.
2026-03-27 04:58:54.1774587534
Let (x+a) be the HCF of $x^2+px+q$ and $x^2+mx+n$. Show that $a=(q-n)/(p-m)$
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hint
$x+a$ divides both polynomials. Hence $x=-a$ is a common root for both. Plug in $x=-a$ in both and subtract.